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Sounds like you have things pretty well in hand. Unless you need that box to be publically accessible though (running a mail server or web server, DNS server etc) I'd just block all external attempts at access as a matter of policy and whitelist specific IP addresses as needed.
If your firewall is worthwhile, it'll drop the ping requests and your server won't respond to port scans. Everyone on the internet gets scanned -- it's just part and parcel of the internet experience. As long as you're properly secured it's nothing to worry about.
As a good faith policy I always look up the owner of the IP and send a 'heads up' email to abuse@ in situations like this. It's not likely to amount to much, especially for traffic originating out of the Ukraine, but it only takes a few seconds and then at least you've done due diligence.
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I wake up in the morning more tired than before I slept
I get through cryin' and I'm sadder than before I wept
I get through thinkin' now, and the thoughts have left my head
I get through speakin' and I can't remember, not a word that I said
- Ben Harper, Show Me A Little Shame
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